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NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 16 ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or “Or”
S.86
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Lesson 16: Solving and Graphing Inequalities Joined by “And” or
“Or”
Classwork
Exercise 1
a. Solve 𝑤2 = 121, for 𝑤. Graph the solution on a number line.
b. Solve 𝑤2 < 121, for 𝑤. Graph the solution on a number line, and write the solution set as a compound
inequality.
c. Solve 𝑤2 ≥ 121, for 𝑤. Graph the solution on a number line, and write the solution set as a compound
inequality.
d. Quickly solve (𝑥 + 7)2 = 121, for 𝑥. Graph the solution on a number line.
e. Use your work from part (d) to quickly graph the solution on a number line to each inequality below.
i. (𝑥 + 7)2 < 121
ii. (𝑥 + 7)2 ≥ 121
NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 16 ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or “Or”
S.87
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exercise 2
Consider the compound inequality −5 < 𝑥 < 4.
a. Rewrite the inequality as a compound statement of inequality.
b. Write a sentence describing the possible values of 𝑥.
c. Graph the solution set on the number line below.
Exercise 3
Consider the compound inequality −5 < 2𝑥 + 1 < 4.
a. Rewrite the inequality as a compound statement of inequality.
b. Solve each inequality for 𝑥. Then, write the solution to the compound inequality.
c. Write a sentence describing the possible values of 𝑥.
d. Graph the solution set on the number line below.
NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 16 ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or “Or”
S.88
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exercise 4
Given 𝑥 < −3 or 𝑥 > −1:
a. What must be true in order for the compound inequality to be a true statement?
b. Write a sentence describing the possible values of 𝑥.
c. Graph the solution set on the number line below.
Exercise 5
Given 𝑥 + 4 < 6 or 𝑥 − 1 > 3:
a. Solve each inequality for 𝑥. Then, write the solution to the compound inequality.
b. Write a sentence describing the possible values of 𝑥.
c. Graph the solution set on the number line below.
NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 16 ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or “Or”
S.89
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exercise 6
Solve each compound inequality for 𝑥, and graph the solution on a number line.
a. 𝑥 + 6 < 8 and 𝑥 − 1 > −1
b. −1 ≤ 3 − 2𝑥 ≤ 10
c. 5𝑥 + 1 < 0 or 8 ≤ 𝑥 − 5
d. 10 > 3𝑥 − 2 or 𝑥 = 4
e. 𝑥 − 2 < 4 or 𝑥 − 2 > 4
f. 𝑥 − 2 ≤ 4 and 𝑥 − 2 ≥ 4
NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 16 ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or “Or”
S.90
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Exercise 7
Solve each compound inequality for 𝑥, and graph the solution on a number line. Pay careful attention to the inequality
symbols and the “and” or “or” statements as you work.
a. 1 + 𝑥 > −4 or 3𝑥 − 6 > −12
b. 1 + 𝑥 > −4 or 3𝑥 − 6 < −12
c. 1 + 𝑥 > 4 and 3𝑥 − 6 < −12
NYS COMMON CORE MATHEMATICS CURRICULUM M1 Lesson 16 ALGEBRA I
Lesson 16: Solving and Graphing Inequalities Joined by “And” or “Or”
S.91
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Problem Set
Solve each inequality for 𝑥, and graph the solution on a number line.
1. 𝑥 − 2 < 6 or 𝑥
3> 4 2. −6 <
𝑥+14
< 3
3. 5𝑥 ≤ 21 + 2𝑥 or 3(𝑥 + 1) ≥ 24
4. 5𝑥 + 2 ≥ 27 and 3𝑥 − 1 < 29
5. 0 ≤ 4𝑥 − 3 ≤ 11
6. 2𝑥 > 8 or −2𝑥 < 4
7. 8 ≥ −2(𝑥 − 9) ≥ −8
8. 4𝑥 + 8 > 2𝑥 − 10 or 1
3𝑥 − 3 < 2
9. 7 − 3𝑥 < 16 and 𝑥 + 12 < −8
10. If the inequalities in Problem 8 were joined by “and” instead of “or,” what would the solution set become?
11. If the inequalities in Problem 9 were joined by “or” instead of “and,” what would the solution set become?
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